×
Kempf, George

The Grothendieck-Cousin complex of an induced representation. (English) Zbl 0393.20027

Adv. Math. 29, 310-396 (1978).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0393.20027

Cited in 1 Review
Cited in 39 Documents

MSC:

20G05 Representation theory for linear algebraic groups
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14M17 Homogeneous spaces and generalizations
14L35 Classical groups (algebro-geometric aspects)
14L15 Group schemes

Keywords:

Induced Representations of a Reductive Algebraic Group; Cousin Complex of a Sheaf on a Filtered Topological Space; H.Weyl’s Character Formula; Local-To-Global Principle; Borel-Weil Vanishing Theorem; Borel Subgroup; Bruhat Cells; Exactness of An Augmented Cousin Complex

Citations:

Zbl 0338.58019; Zbl 0212.216
PDF BibTeX XML Cite
\textit{G. Kempf}, Adv. Math. 29, 310--396 (1978; Zbl 0393.20027)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Baclawski, K.P, Homology and combinatorics of ordered sets, ()
[2] Bernstein, I.I; Gelfand, I.M; Gelfand, S.I, Differential operators on the principal affine space and investigation of g-modules, () · Zbl 0338.58019
[3] Borel, A, Linear algebraic groups, (1969), Benjamin New York · Zbl 0186.33201
[4] Borel, A, Seminar on algebraic groups and related finite groups, ()
[5] Borel, A; Tits, J, Groupes réductifs, Publ. math., IHES, 27, 659-755, (1965) · Zbl 0145.17402
[6] Borel, A, Linear representations of semi-simple algebraic groups, (), 421-440
[7] Bourbaki, N, Groupes et algèbres de Lie, (1968), Hermann Paris, Chaps. IV, V, VI · Zbl 0186.33001
[8] Carter, R; Lusztig, G, On the modular representations of the general linear and symmetric groups, Math. Z., 136, 193-242, (1974) · Zbl 0298.20009
[9] Chevalley, C, Classification des groupes de Lie algébriques, (1956-1958), Inst. H. Poincaré Paris, (poly copiees)
[10] Chevalley, C, Certain schémas de groupes semi-simples, Exp. 219, seminaire bourbaki, (1960-1961)
[11] Demazure, M, “schémas en groupes,” vol. III, () · Zbl 0163.27402
[12] Demazure, M, Une démonstration algébrique d’un théorème de Bott, Invent. math., 5, 349-356, (1968) · Zbl 0204.54102
[13] Demazure, M, Sur la formule des charactères de H. Weyl, Invent. math., 9, 249-252, (1970) · Zbl 0189.21403
[14] Demazure, M, Désingularisation des variétés de Schubert généralisées, Ann. sci. école norm. sup., 7, 53-88, (1974) · Zbl 0312.14009
[15] Godement, R, Topologie algèbrique et théorie des faisceaux, () · Zbl 0080.16201
[16] Grothendieck, A, Éléments de géométrie algébrique, III, Publ. math. IHES, 11 et 17, (1961-1963)
[17] Grothendieck, A, Local cohomology, (), (notes by R. Hartshorne) · Zbl 0185.49202
[18] Grothendieck, A, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et global, (1968), North-Holland Amsterdam
[19] {\scW. Haboush}, unpublished work.
[20] Hartshorne, R, Residues and duality, () · Zbl 0196.24301
[21] Hochster, M, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials and polytopes, Ann. of math., 96, 318-337, (1972) · Zbl 0233.14010
[22] Hochster, M; Roberts, J, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Advances in math., 13, 115-175, (1974) · Zbl 0289.14010
[23] Hochster, M; Roberts, J, The purity of the Frobenius and local cohomology, Advances in math., 21, 117-172, (1976) · Zbl 0348.13007
[24] Iversen, B, The geometry of algebraic groups, Advances in math., 20, 57-85, (1976) · Zbl 0327.14015
[25] Jantzen, J, Zur charakterformel gewisser darstellungen halbeinfacher gruppen und Lie-algebren, Math. Z., 140, 127-149, (1974) · Zbl 0279.20036
[26] Kempf, G, Linear systems on homogeneous spaces, Ann. of math., 103, 557-591, (1976) · Zbl 0327.14016
[27] {\scG. Kempf}, Sóme elementary proofs of basic theorems in the cohomology of quasicoherent sheaves, to appear.
[28] {\scG. Kempf}, The geometry of homogeneous spaces versus induced representation, Amer. J. Math., to appear. · Zbl 0439.14011
[29] Kostant, B, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of math., 74, 329-387, (1961) · Zbl 0134.03501
[30] Macaulay, F.S, The algebraic theory of modular systems, () · Zbl 0802.13001
[31] Mumford, D, Geometric invariant theory, (1965), Springer-Verlag Berlin/New York · Zbl 0147.39304
[32] Mumford́, D, Abelian varieties, (1970), Oxford Univ. Press London, (Tata Lectures) · Zbl 0198.25801
[33] Steinberg, R, Lectures on Chevalley groups, (1967), Yale University
[34] Tits, J, Buildings of spherical type and finite BN-pairs, () · Zbl 0295.20047
[35] Wong, W.J, Representations of Chevalley groups in characteristic p, Nagoya math. J., 45, 39-78, (1972) · Zbl 0214.29003
[36] Popov, V.L, Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles, Izv. akad. nank SSSR, Math. USSR izv., 8, 301-327, (1974) · Zbl 0301.14018
[37] Rosenlicht, M, Toroidal algebraic groups, (), 984-988 · Zbl 0107.14703
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.